## The Contradictory Nature of ZFC Set Theory Rooted in Axiom Creation

What is the basis for reason? And mathematics?

Moderators: AMod, iMod

Eodnhoj7
Posts: 3475
Joined: Mon Mar 13, 2017 3:18 am

### The Contradictory Nature of ZFC Set Theory Rooted in Axiom Creation

The inherent contradictory nature of mathematics lies in the fact "axioms" are created in order to justify it leading to an inherent form of circularity where an axiom creates a framework, the framework is faulty hence a new axiom must be created.

http://gamahucherpress.yellowgum.com/wp ... MATICS.pdf

14
In Burali-fortis day there was a set of all ordinals which resulted in paradox This set has been outlawed in
set theory -because it sends it into self -contradiction. To avoid this paradox mathematicians ad hoc introduced the axiom called the Axiom schema of specification ie axiom of separation

“Modern axiomatic set theory such as ZF and ZFC circumvents this antinomy by simply not allowing construction of sets with unrestricted comprehension terms like "all sets with the property P",” Russell paradox In Russells day there was a set of all sets which destroyed naive set theory-sent it into contradiction-so to avoid it set theory just introduced an axiom Axiom schema of specification ie axiom of
separation Modern set theory just outlaws/blocks/bans this Russells paradox by the introduction of the ad hoc axiom the Axiom schema of specification ie axiom of separationwhich wiki says
http://en.wikipedia.org/wiki/Zermelo%E2 ... set_theory

15"The restriction to z is necessary to avoid Russell's paradox and its variants. " Thus we have two sets - which at one time did exist-which send maths into contradiction just being disallowed by adding an ad hoc axiom IT SHOULD BE NOTED THE IRONY HERE Russell created the axiom
of reducibility to to get rid of paradoxes in mathematics by outlawing impredicative statements but Zermelo created an ad hoc impredicative
axiom the axiom of separation to avoid many paradoxes ie Russell’s paradox Now there is double irony in this as many say Russells axiom of
reducibility should be outlawed as it is ad hoc but the same mathematicians will not say the axiom of separation should be outlawed or dropped as it is
ad hoc –HOW STRANGE Also the ad hoc creation of this impredicative axiom of separation means

1)ZFC is inconsistent

2) that the paradoxes it was meant to avoid are now still valid and thus mathematics is inconsistent As the axiom of ZFC ie axiom of separation outlaws/blocks/bans itself thus making ZFC inconsistent

Proof
http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenk
el_set_theory

### Who is online

Users browsing this forum: No registered users and 2 guests